Reducing synchronization on the parallel Davidson method for the large sparse, eigenvalue problem

• Published in: Proceedings of the 1993 ACM/IEEE conference on Supercomputing pp. 172 - 180
• Main Authors: Stathopoulos, A., Fischer, C. F.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 01.12.1993; IEEE
• Series: ACM Conferences
• Subjects: Chemistry; Computer science; Computer systems organization > Architectures > Distributed architectures > Grid computing; Computer systems organization > Architectures > Parallel architectures; Computer systems organization > Architectures > Parallel architectures > Multicore architectures; Computer systems organization > Architectures > Serial architectures > Superscalar architectures; Computing methodologies > Modeling and simulation > Simulation types and techniques > Massively parallel and high-performance simulations; Eigenvalues and eigenfunctions; High performance computing; Iris; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on matrices; Parallel processing; Physics; Quantum computing; Software and its engineering > Software organization and properties > Software system structures > Distributed systems organizing principles > Grid computing; Sparse matrices; Symmetric matrices
• ISBN: 0818643404; 9780818643408
• ISSN: 1063-9535
• DOI: 10.1145/169627.169685

The Davidson method is extensively used in quantum chemistry and atomic physics for finding a few extreme eigenpairs of a large, sparse, symmetric matrix. It can be viewed as a preconditioned version of the Lanczos method which reduces the number of iterations at the expense of a more complicated step. Frequently, the problem sizes involved demand the use of large multicomputers with hundreds or thousands of processors. The difficulties occurring in parallelizing the Davidson step are dealt with and results on a smaller scale machine are reported. The new version improves the parallel characteristics of the Davidson algorithm and holds promise for a large number of processors. Its stability and reliability is similar to that of the original method.